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A302241 Triangle T(n,k) read by rows giving the coefficients of the matching-generating polynomial of the n X n knight graph (0 <= k <= floor(n^2/2)).

%I A302241 #9 Feb 16 2025 08:33:53
%S A302241 1,1,1,8,20,16,2,1,24,224,1032,2464,2944,1592,320,16,1,48,964,10592,
%T A302241 70024,289344,754244,1226288,1203410,670000,189544,22112,644,1,80,
%U A302241 2828,58432,786982,7298848,48033800,227891056,784428297,1956801264,3509779148,4458911088,3919123796,2301829920,858287984,187915392,21263600,980608,10304
%N A302241 Triangle T(n,k) read by rows giving the coefficients of the matching-generating polynomial of the n X n knight graph (0 <= k <= floor(n^2/2)).
%H A302241 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnightGraph.html">Knight Graph</a>
%H A302241 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Matching-GeneratingPolynomial.html">Matching-Generating Polynomial</a>
%e A302241 Rows as polynomials:
%e A302241 1,
%e A302241 1,
%e A302241 1 + 8*x + 20*x^2 + 16*x^3 + 2*x^4,
%e A302241 1 + 24*x + 224*x^2 + 1032*x^3 + 2464*x^4 + 2944*x^5 + 1592*x^6 + 320*x^7 + 16*x^8,
%e A302241 1 + 48*x + 964*x^2 + 10592*x^3 + 70024*x^4 + 289344*x^5 + 754244*x^6 + 1226288*x^7 + 1203410*x^8 + 670000*x^9 + 189544*x^10 + 22112*x^11 + 644*x^12,
%e A302241 ...
%Y A302241 Row sums are A287225.
%K A302241 nonn,tabl
%O A302241 1,4
%A A302241 _Eric W. Weisstein_, Apr 03 2018